Method for forecasting second-order wave force value of ship in maneuvering state

Abstract

The invention discloses a ship second-order wave force numerical forecasting method in a maneuvering state, and the method comprises the following steps: S01, reading calculation parameters including ship body grids, navigational speed and frequency, extracting ship body waterline information based on discrete grids, and calculating object plane normal vector n and m items; s02, solving a flow velocity potential by using a high-order analysis moving pulsation source method; s03, calculating a hydrodynamic coefficient, a wave exciting force and a motion response; and S04, forecasting the second-order wave force of the ship in the maneuvering state. By means of the method, reasonable, efficient and practical numerical forecasting can be provided for longitudinal, transverse and yawing second-order force (moment) caused by waves in maneuvering states such as forward / oblique navigation of the ship.

Description

Technical Field

[0001] The invention relates to the technical field of wave force numerical prediction, and in particular to a method for numerically predicting second-order wave force of a ship in a maneuvering state. Background Art

[0002] Maneuverability is one of the most important navigation performances of ships. It reflects the ability of ships to change their motion state quickly and accurately according to the requirements of the driver to avoid obstacles or other ships on the preset route. Its quality is directly related to the safety of the ship. Most of the traditional studies on ship maneuverability are aimed at the movement in still water. These studies provide a reliable basis for the maneuverability evaluation in the ship design stage to a certain extent. However, unlike still water, ships will always encounter waves when sailing on the sea. The swaying motion and second-order wave drift force caused by this will lead to poor maneuverability of the ship, and the propulsion efficiency and rudder efficiency will be sharply reduced. In some extreme cases, it may even cause the ship to swing sideways and drift, causing capsizing or collision accidents. Therefore, it is of great significance to carry out in-depth and systematic research on the hydrodynamic performance of ships in maneuvering states in waves, and to efficiently and accurately predict ship motion and second-order wave forces, in order to ensure the rational design of ships and safe and reliable navigation.

[0003] However, there is still no perfect analysis and prediction method for the second-order forces (torques) caused by waves when the ship is in a maneuvering state. At present, the CFD method based on the viscous flow theory has too much computational complexity in wave-related simulations. Even for a simple problem of a ship sailing in a linear regular wave, the calculation time for a single working condition is measured in days, and the real-time prediction of motion and second-order wave loads under complex sea conditions is even more difficult to achieve; the two-dimensional slice theory uses the slenderness of the hull to transform the three-dimensional problem into a two-dimensional problem for solution, so the calculation is simpler and more efficient, but the high frequency, low speed, slenderness assumption of the hull and the inability to handle longitudinal motion of this method limit its further development and application; the three-dimensional Rankine source method can flexibly handle different forms of boundary conditions and is more suitable for nonlinear ship hydrodynamic analysis, but when solving it, on the one hand, it needs to truncate the infinitely wide free surface, which will cause truncation errors and difficult to meet the radiation conditions at the truncation point; on the other hand, it needs to discretize the free surface, which has low computational efficiency and lacks engineering practicality.

[0004] How to solve the above technical problems and make calculations simpler and faster is the direction that technical personnel in the field are committed to research. Summary of the invention

[0005] The purpose of the invention is to provide a method for numerically predicting the second-order wave force of a ship in a maneuvering state.

[0006] In order to solve the above technical problems, the present invention is achieved through the following technical solutions:

[0007] A method for numerically predicting second-order wave forces of a ship in a maneuvering state comprises the following steps:

[0008] S01, read in the calculation parameters including the hull mesh, speed and frequency, wherein the hull mesh is a nine-node isoparametric unit, and based on the discrete mesh, extract the hull waterline information, and calculate the object surface normal vector n and m;

[0009] S02, solve the process velocity potential using a high-order analytical moving pulsating source method;

[0010] S03, calculate the hydrodynamic coefficients, wave excitation forces and motion response;

[0011] S04, prediction of second-order wave forces on ships in maneuvering state.

[0012] As a specific implementation method, in the process of solving step S02, the surface integral of the product of the velocity potential and the normal derivative of the Green's function in each high-order unit is The surface integral of the product of the normal derivative of the velocity potential and the Green's function The calculation formula is as follows,

[0013]

[0014] In the formula, and are the velocity potential and its normal derivative at the kth node in the nine-node high-order element; α is a constant coefficient related to the node coordinates;

[0015]

[0016] and are the slope and intercept of the ith edge of the higher-order unit, respectively; n1, n2, n3 are the components of the normal vector of the surface element along the x, y, z axis of the rectangular coordinate system, respectively; μ n '=g2-i[e2cosθ+(-1) n-1 f2sinθ], where τ is the Brard number; g1, g2, e1, e2, f1, f2 are constant coefficients that depend on the angle between the surface element and the coordinate plane; Where g is the acceleration of gravity, and U is the ship's sailing speed; and They are and The integral of , where E1() is a complex exponential integral function; δ mn is a step function; β mn =(z+ζ)+i[(x-ξ)cosθ+(-1) n-1(y-η)sinθ], where (x, y, z) and (ξ, η, ζ) are the coordinates of the field point and the source point respectively; η' is the coordinate of the source point in the local coordinate system with the centroid of the surface element as the coordinate origin); and lnβ n ,η'lnβ n and η' 2 lnβ n The integral of and They are β n and η'β n The integral of k 、b k 、c k Represents the coefficient related to the unit node coordinates, C n '=g2-i[e2cosθ+(-1) n-1 f2sinθ],D n = z + ζ0 + i [(x - ξ0) cos θ + (-1) n-1 (y-η0)sinθ], (ξ0,η0,ζ0) represent the coordinates of the centroid of the surface element.

[0017] As a specific implementation, in step S03, after the velocity potential in the flow field is obtained in step S02, the pressure on the hull surface is calculated to obtain the fluid force acting on the ship, and the fluid force acting on the ship is decomposed into incident force, diffraction force, radiation force and static restoring force, wherein:

[0018] The calculation formula for the component of the incident force acting on the ship along the direction i (i = 1, 2, ..., 6) is:

[0019]

[0020] Where: ω0 represents the incident wave frequency; ω e Indicates the frequency of ship encounters; represents the incident wave velocity potential; ρ is the water density; S B is the average wetted surface of the ship; F i I is the component of the incident force acting on the ship along the i direction; is the corresponding complex amplitude; t represents time; ni represents the component of the normal vector along the direction i (i = 1, 2, ..., 6); e is a constant coefficient; dS represents the area integral;

[0021] The calculation formula for the component of the diffraction force acting on the ship along the direction i (i = 1, 2, ..., 6) is:

[0022]

[0023] Where: F i D is the component of the diffraction force on the ship along the i direction; f i D is the corresponding complex amplitude; is the diffraction potential;

[0024] The calculation formula of ship hydrodynamic coefficient is:

[0025]

[0026] Where: is the radiation potential of the ship; μ ij and λ ij are the added mass and damping coefficient respectively;

[0027] After obtaining the incident force, diffraction force and hydrodynamic coefficient on the ship, the motion response of the ship is calculated by the following formula:

[0028]

[0029] Where: {m ij} is the inertia matrix of the ship; is the equivalent linearized viscous damping coefficient; c ij is the restoring force coefficient; X j represents the complex motion amplitude of the jth mode, j = 1, 2, ..., 6 corresponds to surge, sway, heave, roll, pitch and yaw, respectively, δ 4j represents the Kronecker symbol, f i F-K Represents the incident wave force, and solving the above six-variable linear equations can obtain the ship's rolling motion displacement.

[0030] As a specific implementation, in step S04, the second-order wave force and moment formula is as follows:

[0031]

[0032] Where: F represents the second-order wave force, M z represents the second-order wave moment;

[0033]

[0034] k is the wave number of the incident wave; is the conjugate complex number of the incident potential φ0; f i F-K The conjugate complex number of ; β is the wave angle; L is the ship length; b(x) is the half width of the ship at coordinate x; X3 and X5 represent heave and pitch motions;

[0035] When the incident wavelength is short wave, the short wave second-order force is corrected:

[0036]

[0037] Where: F A represents the longitudinal second-order wave force,

[0038]

[0039] (1+α U )=1+C U Fn,C U =max[10.0,-310B f (β)+68], dl represents the integral about the waterline; F n represents the Froude number; I1 represents the first-order modified Bessel function of the first kind, χ is the angle between the tangent of the waterline and the x-axis, and B represents the ship width.

[0040] Compared with the prior art, the present invention is beneficial in that:

[0041] 1) The numerical prediction method for the second-order wave force of a ship in a maneuvering state described in the present invention is based on the Green's function of a moving pulsating source and high-order surface element discretization, and a stable, accurate and efficient semi-analytical high-order moving pulsating source method is established. According to the spatial distribution characteristics of the Green's function of the moving pulsating source, the method derives the analytical single integral formula of the Green's function of the moving pulsating source on the high-order unit by exchanging the integration order and using the Newton-Leibniz formula, thereby solving the problems of instability, inaccuracy and low efficiency in the numerical solution process, thereby providing a new, more reliable and efficient theoretical model and numerical method for the study of hydrodynamic problems of ships sailing in waves;

[0042] 2) The present invention studies and develops a method and a prediction program for calculating the second-order wave forces in all wave directions and frequencies when the ship is maneuvering in waves. Based on the hydrodynamic and motion responses obtained by the analytical high-order moving pulsating source method, and referring to the derivation process of the traditional Salvensen method for calculating the second-order wave forces based on the slice theory, a calculation expression for the second-order forces is established within the framework of the three-dimensional potential flow theory. At the same time, in order to make up for its shortcomings in short waves, the above formula is further combined with the existing semi-empirical formula in engineering, thereby establishing a hybrid method that can be used for calculating the second-order wave forces in all wave directions and frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0044] Figure 1 It is a calculation flow chart of the numerical prediction method of the second-order wave force of a ship in a maneuvering state according to the present invention;

[0045] Figure 2 A schematic diagram of a coordinate system and a waterline for the correction calculation of short-wave second-order forces in the numerical prediction method for second-order wave forces of ships in a maneuvering state described in the present invention;

[0046] Figure 3 is a ship type line diagram of a bulk carrier in Example 1;

[0047] Figure 4 is the longitudinal second-order wave force diagram of a bulk carrier sailing in regular waves at a speed of 15 kn in Example 1;

[0048] Figure 5 The diagram is a diagram of the second-order lateral force and the second-order moment in the yaw direction received by a bulk carrier in Example 1 when sailing in regular waves with a wave angle of 135°. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention:

[0050] The present invention provides a method for numerically predicting second-order wave forces of a ship in a maneuvering state, comprising the following steps:

[0051] S01, read in the calculation parameters including the hull mesh, speed and frequency, wherein the hull mesh is a nine-node isoparametric unit, and based on the discrete mesh, extract the hull waterline information, and calculate the object surface normal vector n and m.

[0052] S02, solve the process velocity potential using a high-order analytical moving pulsating source method;

[0053] The core idea of ​​the high-order analytical moving pulsation source method is to construct the boundary integral equation with the moving pulsation source Green's function as the kernel function. When solving the numerical problem, a nine-node high-order unit is used to discretize the boundary, and an analytical method is used to calculate the surface integral of the free surface Green's function to improve the stability and efficiency of the numerical calculation.

[0054] The key to solving the above method is to calculate the surface integral of the product of the velocity potential and the normal derivative of the Green's function in each high-order unit. The surface integral of the product of the normal derivative of the velocity potential and the Green's function The present invention proposes an analytical method to calculate it. The calculation formula is as follows:

[0055]

[0056] In the formula, and are the velocity potential and its normal derivative at the kth node in the nine-node high-order element; α is a constant coefficient related to the node coordinates;

[0057]

[0058] and are the slope and intercept of the ith edge of the higher-order unit, respectively; n1, n2, n3 are the components of the normal vector of the surface element along the x, y, z axis of the rectangular coordinate system, respectively; μ n '=g2-i[e2cosθ+(-1) n-1 f2sinθ], where τ is the Brard number; g1, g2, e1, e2, f1, f2 are constant coefficients that depend on the angle between the surface element and the coordinate plane; Where g is the acceleration of gravity, and U is the ship's sailing speed; and They are and The integral of , where E1() is a complex exponential integral function; δ mn is a step function; β mn =(z+ζ)+i[(x-ξ)cosθ+(-1) n-1 (y-η]sinθ], where (x, y, z) and (ξ, η, ζ) are the coordinates of the field point and the source point respectively; η' is the coordinate of the source point in the local coordinate system with the centroid of the surface element as the coordinate origin); and lnβ n ,η'lnβ n and η' 2 lnβ n The integral of and β n and η'β n The integral of k 、b k 、c k Represents the coefficient related to the unit node coordinates, Cn '=g2-i[e2cosθ+(-1) n-1 f2sinθ],D n = z + ζ0 + i [(x - ξ0) cos θ + (-1) n-1 (y-η0)sinθ], (ζ0,η0,ζ0) represents the coordinates of the centroid of the surface element.

[0059] S03, calculate the hydrodynamic coefficients, wave excitation forces and motion response;

[0060] After the velocity potential in the flow field is obtained in step S02, the pressure on the hull surface is calculated to obtain the fluid force acting on the ship. The fluid force acting on the ship is decomposed into incident force, diffraction force, radiation force and static restoring force, where:

[0061] The calculation formula for the component of the incident force acting on the ship along the direction i (i = 1, 2, ..., 6) is:

[0062]

[0063] Where: ω0 represents the incident wave frequency; ω e Indicates the frequency of ship encounters; represents the incident wave velocity potential; ρ is the water density; S B is the average wetted surface of the ship; F i I is the component of the incident force acting on the ship along the i direction; is the corresponding complex amplitude; t represents time; ni represents the component of the normal vector along the direction i (i = 1, 2, ..., 6); e is a constant coefficient; dS represents the area integral;

[0064] The calculation formula for the component of the diffraction force acting on the ship along the direction i (i = 1, 2, ..., 6) is:

[0065]

[0066] Where: F i D is the component of the diffraction force on the ship along the i direction; f i D is the corresponding complex amplitude; is the diffraction potential;

[0067] The calculation formula of ship hydrodynamic coefficient is:

[0068]

[0069] Where: is the radiation potential of the ship; μ ij and λij are the added mass and damping coefficient respectively;

[0070] After obtaining the incident force, diffraction force and hydrodynamic coefficient on the ship, the motion response of the ship is calculated by the following formula:

[0071]

[0072] Where: {m ij} is the inertia matrix of the ship; is the equivalent linearized viscous damping coefficient; c ij is the restoring force coefficient; X j represents the complex motion amplitude of the jth mode, j = 1, 2, ..., 6 corresponds to surge, sway, heave, roll, pitch and yaw, respectively, δ 4j represents the Kronecker symbol, f i F-K Represents the incident wave force, and solving the above six-variable linear equations can obtain the ship's rolling motion displacement.

[0073] S04, prediction of second-order wave forces on ships in maneuvering state.

[0074] The calculation method of the second-order force used here is established by referring to the process of Salvesen's derivation of the second-order wave force calculation formula based on the slice theory. In order to obtain the calculation formula of the second-order wave force, firstly, within the scope of potential flow theory, the calculation formula of the fluid force acting on the ship is obtained by integrating the pressure along the instantaneous wet surface of the hull, and then, it is processed in turn using the Reynolds transport theorem, Gauss's theorem, gradient operation rule, etc., so as to obtain the following calculation formula of the second-order force and moment:

[0075]

[0076] Where: F represents the second-order wave force, M z represents the second-order wave moment

[0077]

[0078]

[0079] k is the wave number of the incident wave; is the conjugate complex number of the incident potential φ0; f i F-K The conjugate complex number of ; β is the wave angle; L is the ship length; b(x) is the half width of the ship at coordinate x; X3 and X5 represent heave and pitch motions;

[0080] The calculation formula of the above average second-order force is established within the scope of linear potential flow theory. When the incident wavelength is short, the formula is not applicable due to the large nonlinear effect. In view of this, scholars have proposed many empirical or semi-empirical methods to calculate short-wave second-order wave forces. The present invention adopts the following semi-empirical method that is applicable to both fat ships and slender ships to correct the short-wave second-order force.

[0081] k is the wave number of the incident wave; is the conjugate complex number of the incident potential φ0; f i F-K The conjugate complex number of ; β is the wave angle; L is the ship length; b(x) is the half width of the ship at coordinate x; X3 and X5 represent heave and pitch motions;

[0082] When the incident wavelength is short wave, the short wave second-order force is corrected:

[0083]

[0084] Where: F A represents the longitudinal second-order wave force,

[0085]

[0086] (1+α U )=1+C U Fn,C U =max[10.0,-310B f (β)+68], dl represents the integral about the waterline; F n represents the Froude number; I1 represents the first-order modified Bessel function of the first kind, χ is the angle between the tangent of the waterline and the x-axis, B represents the ship's width, and the schematic diagram of the waterline and coordinate system can be found in Figure 2 shown.

[0087] Example 1

[0088] In this example, the sway response of a bulk carrier is predicted based on the numerical prediction method of the second-order wave force of ships under the maneuvering state. The main dimensions and calculation conditions of the bulk carrier are shown in Table 1, and the line diagram is shown in Figure 3 .

[0089] Table 1 Main dimensions and calculation conditions of a bulk carrier

[0090]

[0091] The prediction method of the present invention is used to calculate the second-order wave forces and moments of the bulk carrier when it sails at a speed of 15 kn and in two different wave directions (135° and 180°) in waves of a series of different wavelengths (0<λ / L<2.5), and the correctness of the method proposed in the present invention is verified by comparing with the results of the water tank model test.

[0092] Figure 4 and 5 The calculation results of the second-order forces (moments) in the longitudinal, transverse and yaw directions of a bulk carrier sailing at a speed of 15 kn in waves with wave angles of 180° and 135° are given, as well as their comparison curves with the experimental values. Figure 5 In the figure, (a) represents the lateral second-order force; (b) represents the second-order moment in the yaw direction. From the comparison results, it can be seen that the second-order force results of the ship obtained by the prediction method of the present invention are in good agreement with the model test results, which verifies its reliability.

[0093] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of this case.

Claims

1. A numerical prediction method for second-order wave forces of ships in maneuvering state, characterized in that: The following steps are involved: S01, read in the calculation parameters including the hull mesh, speed and frequency, wherein the hull mesh is a nine-node isoparametric unit, and based on the discrete mesh, extract the hull waterline information, and calculate the object surface normal vector n and m; S02, solve the process velocity potential using a high-order analytical moving pulsating source method; S03, calculate the hydrodynamic coefficients, wave excitation forces and motion response; S04, prediction of second-order wave forces on ships in maneuvering state.

2. The method for numerical prediction of second-order wave forces of ships in maneuvering state according to claim 1 is characterized in that: In the process of solving step S02, the surface integral of the product of the velocity potential and the normal derivative of the Green's function in each high-order unit is The surface integral of the product of the normal derivative of the velocity potential and the Green's function The calculation formula is as follows, In the formula, and are the velocity potential and its normal derivative at the kth node in the nine-node high-order element; α is a constant coefficient related to the node coordinates; and are the slope and intercept of the ith edge of the higher-order unit, respectively; n1, n2, n3 are the components of the normal vector of the surface element along the x, y, z axis of the rectangular coordinate system, respectively; μ n '=g2-i[e2cosθ+(-1) n- 1 f2sinθ], where τ is the Brard number; g1, g2, e1, e2, f1, f2 are constant coefficients that depend on the angle between the surface element and the coordinate plane; Where g is the acceleration of gravity, and U is the ship's sailing speed; and They are and The integral of , where E1() is a complex exponential integral function; δ mn is a step function; β mn =(z+ζ)+i[(x-ξ)cosθ+(-1) n-1 (y-η)sinθ], where (x, y, z) and (ξ, η, ζ) are the coordinates of the field point and the source point respectively; η' is the coordinate of the source point in the local coordinate system with the centroid of the surface element as the coordinate origin); and lnβ n ,η'lnβ n and η' 2 lnβ n The integral of and They are β n and η'β n The integral of k , b k 、c k Represents the coefficient related to the unit node coordinates, C n '=g2-i[e2cosθ+(-1) n-1 f2sinθ],D n = z + ζ0 + i [(x - ξ0) cos θ + (-1) n-1 (y-η0)sinθ], (ξ0,η0,ζ0) represent the coordinates of the centroid of the surface element.

3. The method for numerical prediction of second-order wave forces of ships in maneuvering state according to claim 1 is characterized in that: In step S03, after the velocity potential in the flow field is obtained in step S02, the pressure on the hull surface is calculated to obtain the fluid force acting on the ship, and the fluid force acting on the ship is decomposed into incident force, diffraction force, radiation force and static restoring force, wherein: The calculation formula for the component of the incident force acting on the ship along the direction i (i = 1, 2, ..., 6) is: Where: ω0 represents the incident wave frequency; ω e Indicates the frequency of ship encounters; represents the incident wave velocity potential; ρ is the water density; S B is the average wetted surface of the ship; F i I is the component of the incident force acting on the ship along the i direction; f i I is the corresponding complex amplitude; t represents time; ni represents the component of the normal vector along the direction i (i = 1, 2, ..., 6); e is a constant coefficient; dS represents the area integral; The calculation formula for the component of the diffraction force acting on the ship along the direction i (i = 1, 2, ..., 6) is: Where: F i D is the component of the diffraction force on the ship along the i direction; f i D is the corresponding complex amplitude; is the diffraction potential; The calculation formula of ship hydrodynamic coefficient is: Where: is the radiation potential of the ship; μ ij and λ ij are the added mass and damping coefficient respectively; After obtaining the incident force, diffraction force and hydrodynamic coefficient on the ship, the motion response of the ship is calculated by the following formula: Where: {m ij } is the inertia matrix of the ship; is the equivalent linearized viscous damping coefficient; c ij is the restoring force coefficient; X j represents the complex motion amplitude of the jth mode, j = 1, 2, ..., 6 corresponds to surge, sway, heave, roll, pitch and yaw, respectively, δ 4j represents the Kronecker symbol, f i F-K Represents the incident wave force, and solving the above six-variable linear equations can obtain the ship's rolling motion displacement.

4. The method for numerical prediction of second-order wave forces of ships in maneuvering state according to claim 1 is characterized in that: In step S04, the second-order wave force and moment formula is as follows: Where: F represents the second-order wave force, M z represents the second-order wave moment; k is the wave number of the incident wave; is the conjugate complex number of the incident potential φ0; (f j F-K ) * f i F-K The conjugate complex number of ; β is the wave angle; L is the ship length; b(x) is the half width of the ship at coordinate x; X3 and X5 represent heave and pitch motions; When the incident wavelength is short wave, the short wave second-order force is corrected: Where: F A represents the longitudinal second-order wave force, (1+α U )=1+C U Fn,C U =max[10.0,-310B f (β)+68], dl represents the integral about the waterline; F n represents the Froude number; I1 represents the first-order modified Bessel function of the first kind, χ is the angle between the tangent of the waterline and the x-axis, and B represents the ship width.

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